if y⁻⁴ = 256 then y will be
Answer:
y = 1/4
Step-by-step explanation:
y⁻⁴ = 256
(1/y)⁴ = 256
y⁴ = 1/256
y = ⁴√1/256
y = 1/4
Thus, The value of y is 1/4
-TheUnknownScientist
Find a positive number for which the sum of it and its reciprocal is the smallest (least) possible. Let x be the number and let S be the sum of the number and its reciprocal. Write the objective function in terms of x. S(x) nothing The interval of interest of the objective function is nothing. (Simplify your answer. Type your answer in interval notation.) The number is 0.
Answer:
[tex]S(x) = x + \frac{1}{x}[/tex] --- Objective function
Interval = [tex]\{x:x=1\}[/tex]
Step-by-step explanation:
Given
Represent the number with x
The required sum can be represented as:
[tex]x + \frac{1}{x}[/tex]
Hence, the objective function is:
[tex]S(x) = x + \frac{1}{x}[/tex]
To get the the interval, we start by differentiating w.r.t x
Using first principle, this gives:
[tex]S'(x) = 1 - \frac{1}{x^2}[/tex]
Equate S'(x) to 0 in order to solve for x
[tex]0 = 1 - \frac{1}{x^2}[/tex]
Subtract 1 from both sides
[tex]0 -1 = 1 -1 - \frac{1}{x^2}[/tex]
[tex]-1 = - \frac{1}{x^2}[/tex]
Multiply both sides by -1
[tex]1 = \frac{1}{x^2}[/tex]
Cross Multiply
[tex]x^2 * 1 = 1[/tex]
[tex]x^2 = 1[/tex]
Take positive square root of both sides because x is positive
[tex]\sqrt{x^2} = \sqrt{1[/tex]
[tex]x = 1[/tex]
Representing x using interval notation, we have
Interval = [tex]\{x:x=1\}[/tex]
To get the smallest sum, we substitute 1 for x in [tex]S(x) = x + \frac{1}{x}[/tex]
[tex]S(1) = 1 + \frac{1}{1}[/tex]
[tex]S(1) = 1 + 1[/tex]
[tex]S(1) = 2[/tex]
Hence, the smallest sum is 2
b. Were you able to find the solution(s) of each Mathematical sentence? How did
you find the solution(s) of each Mathematical sentence?
pls,,, help me mga tol
Answer:
Evaluate each given numbers, expressions or equation.
Check the values or numbers.
Now in order to solve we proceed in the manner
Read the problem Analyze the problem Write the given variables Find the missing variables Write the equation Solve the equation
(2,8),(7,8) slope of the line
Answer:
The slope of line is 0 given points (2,8)(7,8)
Step-by-step explanation:
We need to find slope of line given points (2,8),(7,8)
The formula used to find slope of line is: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
We are given:
[tex]x_1=2, y_1=8, x_2=7 \ and \ y_2=8[/tex]
Finding slope using formula:
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{8-8}{7-2}\\Slope=\frac{0}{5}\\Slope=0[/tex]
So, the slope of line is 0
(HELP ASAP ILL GIVE BRAINIEST)
Graph h(x) = { x +4.
The attached picture is the graph of:
[tex]h(x)=\frac{2}{3} +4[/tex]
what 4p-5(p+6)simplified
Answer: -p - 30
Step-by-step explanation:
What is the answer to x - 10 + -6 + 4
Answer: x-12
Step-by-step explanation:
Simplify.
x
−
1
0
−
6
+
4
x−10−6+4
2 Collect like terms.
x
+
(
−
1
0
−
6
+
4
)
x+(−10−6+4)
3 Simplify.
x
−
1
2
x−12
2r-7 = r + 15,
Find R
Answer: 22
Step-by-step explanation:
2r - 7 = r + 15
2r - r = 15 + 7
2r = 22
r = 22/2
r = 11
find the value of x of given figure and solve this question step by step plzz help question number D
Answer:
x=15 cm
Step-by-step explanation:
The two triangles in the diagram are:
ABC and BDC
First we have to find the third side (hypotenuse) of BDC so that we can use it to find the value of x.
Hypotenuse is the largest side of a triangle which is usually in front of the right angle.
So in BDC
[tex]Base = BD =10cm\\Hypotenuse = BC = ?\\Perpendicular = CD = 2\sqrt{11}cm[/tex]
Applying Pythagoras theorem:
[tex](Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2\\BC^2 = BD^2 + CD^2\\BC^2 = (10)^2 + (2\sqrt{11})^2\\BC^2 = 100+(2^2 * 11)\\BC^2 = 100+(4*11)\\BC^2 = 100+44\\BC^2 = 144\\\sqrt{BC^2} = \sqrt{144}\\BC = 12cm[/tex]
Solving for triangle ABC
[tex]Base = BC = 12 cm\\Perpendicular = AB = 9 cm\\Hypotenuse = AC = x\\[/tex]
Applying Pythagoras theorem
[tex]AC^2 = BC^2+AB^2\\x^2 = (12)^2 + (9)^2\\x^2 = 144+81\\x^2 = 225\\\sqrt{x^2} = \sqrt{225}\\x = 15cm[/tex]
Hence,
x=15 cm
An object travels in a straight line for 1200 m in 20 seconds. What is the average velocity? *
Answer:
Velocity is 20
Step-by-step explanation:
well you divide the meters traveled by the time it took and you should get your answer.
1. divide 1200 by 20
2 answer should be 60
Will someone help me please please please please :D
Answer:
I believe it's C, 0.4 x 0.7
Step-by-step explanation:
A polyhedron with two parallel congruent faces called bases connected by parallelogram faces is called a...
Answer:
right prism
Step-by-step explanation:
If the faces are rectangles, then this prism is called a "right prism"
Which statements are true? Select the five correct answers. StartRoot 1.8 EndRoot < 1.8 StartRoot 1.8 EndRoot greater-than 1 StartRoot 1.8 EndRoot less-than StartRoot 1.9 EndRoot 1.3 less-than StartRoot 1.8 EndRoot less-than 1.4 StartRoot 1.9 EndRoot + StartRoot 1.8 EndRoot greater-than 2 StartRoot 1.9 EndRoot minus StartRoot 1.8 EndRoot greater-than 0.1
Answer:
A,B,C,D,E
Step-by-step explanation:
Answer:
a b c d e
Step-by-step explanation:
edge 2023
Two cases of cans weigh 32 lbs. How much do 7 cases weigh?
Answer:
112 lbs
Step-by-step explanation:
32/2 = 16 lbs
16*7 lbs = 112 lbs
PLS GIVE BRAINLIEST
helllllllppppp me please
Answer:
no
Step-by-step explanation:
4(x+8)+9(6-2x)
plz explain me step by step plz answer me fast
Answer:
86-14x
Step-by-step explanation:
4(x+8)+9(6-2x)
4x-18x+54
4x-18x+86
-14x+86
86-14x
i am currently struggling on number 5
Answer:
7 and 5 also 3 probably I guess
Hi, this is apart of my homework assignment!
The Directions are, “Find the Percent Change. Specify an increase or a decrease.”
13. original amount: 25
amount of increase: 4
This is worth 12 pts!
Answer:
Percent Change is 16%
The change is increased.
Step-by-step explanation:
The original amount = 25
Amount increase = 4
We need to find percent increase
The formula used is: [tex]\frac{Amount \ increased}{Original \ Amount}*100[/tex]
Putting values in formula
[tex]Percent \ Change = \frac{Amount \ increased}{Original \ Amount}*100\\Percent \ Change =\frac{4}{25}*100\\Percent \ Change =16 \%[/tex]
So, Percent Change is 16%
The change is increased.
Use an exponent to write each expression 7/9 x 7/9 x 7/9 x 7/9 x 7/9 x 7/9 x 7/9 x 7/9
Point A is located at (-4, -5). After it is translated, point A' is located at (-4, 1). What was the translation?
6 units down
6 units up
6 units to the left
6 units to the right
Answer: 6 units up
Step-by-step explanation:
because -5 +6 is 1, we know that the translation is 6 units up
i am dumb pleasle help
The ratio of white socks to brown socks is
Answer:
3:2 is the ratio.
Step-by-step explanation:
Given mn, find the value of x.
Answer: x = 15
we have: (6x - 5)° + (6x + 5)° = 180°
⇔ 12x = 180
⇔ x = 180/12=15
Step-by-step explanation:
Using long division, what are the first 4 digits in converting
13/33
to decimal form?
Answer:
0.3939
Step-by-step explanation:
Addition and Subtraction of Mixed Numbers.
8 7/8+(7 5/6−2 1/3)
Answer:
14 1/3
Step-by-step explanation:
First, you need to do what's in the parenthesis by finding a common denominator, which is 6. Multiply the 1 by 2 because that is what you multiply 3 by to get 6. You end up with 8 7/8 + 5 3/6. You then have to find the common denominator again, which is 24. Now the problem is 8 21/24 + 5 12/24. you get 13 32/24, which is equal to 14 8/24. Simplify, and you have 14 1/3.
On a loan of $3520.10, if the one-time simple interest was at 7.77% of the principal, how much interest was incurred?
Answer:
Step-by-step explanation:
3520.10*7.77%= $273.51
Read this introduction to a magazine article
What will most likely be included in the magazine
article that follows this introduction?
Summertime is near, and the lifeguard's whistle
beckons. It is almost time for the swimming season of
course, with swimming season comes slippery pool
decks and shallow water at the end of some docks And
there are always a few swimmers who overestimate
their skills or underestimate their fatigue
O the benefits of swimming
a technical description of strokes
water-safety suggestions
water-centered vacation destinations
Jp
Answer:
water-safety suggestions
Explanation:
We can make this conclusion because we notice this addition from the opening lines of the article, "Summertime is near, the lifeguard's whistle beckons.."
By such Inclusion, the article in other words is saying that since during summertime many people go swimming, it would be best to follow some water-safety suggestions. Therefore, it is most likely to be included in the magazine.
Answer:
water-safety suggestions
Step-by-step explanation:
When finding the slope of a line using a slope triangle, the____
length is divided by the____
length.
Answer:
rise, run
Step-by-step explanation:
When finding the slope of a line using a slope triangle, the RISE length is divided by the RUN length. (I think. Sometimes the "divided by" makes me confused about which is on top, but I'm pretty sure this is right.)
3x + 2 y = 8
5x + 2 y = 12
What is the solution of the system of equations shown above?
Answer:
x = -3
Step-by-step explanation:
First solve it:
Subtract the x's from both sides
2y = -3x +8
2y = -5x +2
Divide by two
y= -1.5x + 4
y = -2.5x +1
set them equal to each other:
-1.5x +4 = -2.5x +1
Add 2.5 x to both sides
1x +4 = 1
x +4 = 1
subtract 4 from both sides
x = -3
Jordan weighed two buckets of sand for a geology project. The first bucket weighed 26.31 pounds. The other bucket weighed 4.39 pounds. How much do the two buckets of sand weigh all together?
Answer:
30.7
Step-by-step explanation:
How can I isolate the variable f in f/3 + 22 = 17
Answer: First You Have To Simplify The Equation From Both Sides Then Thats how You Will Determine what f is. F = -15
Variable [tex]f[/tex] is isolated as [tex]\boldsymbol{f=-15}[/tex] in the expression [tex]\frac{f}{3}+22=17[/tex].
VariableA variable is a symbol and placeholder for a changing amount or any mathematical object.
An algebraic expression is one that is composed of integer constants, variables, and algebraic operations.
Given expression is [tex]\frac{f}{3}+22=17[/tex]
Transpose [tex]22[/tex] to the right side of the equation.
[tex]\frac{f}{3}=17-22\\\frac{f}{3}=-5[/tex]
[tex]f=-15[/tex]
So, variable [tex]f[/tex] is isolated as [tex]\boldsymbol{f=-15}[/tex]
Find out more information about algebraic expression here:
https://brainly.com/question/2945451?referrer=searchResults